Toward a Universal Mapping Algorithm for Accessing Trees in Parallel Memory Systems (1998)
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BibTeX
@MISC{Auletta98towarda,
author = {Vincenzo Auletta and Sajal K. Das and Amelia De Vivo and M. Cristina Pinotti and Vittorio Scarano},
title = {Toward a Universal Mapping Algorithm for Accessing Trees in Parallel Memory Systems},
year = {1998}
}
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Abstract
We study the problem of mapping the N nodes of a complete t-ary tree on M memory modules so that they can be accessed in parallel by templates, i.e. distinct sets of nodes. Typical templates for accessing trees are subtrees, root-to-leaf paths, or levels which will be referred to as elementary templates. In this paper, we first propose a new mapping algorithm for accessing both paths and subtrees of size M with an optimal number of conflicts (i.e., only one conflict) when the number of memory modules is limited to M . We also propose another mapping algorithm for a composite template, say V (as versatile), such that its size is not fixed and an instance of V is composed of any combination of c instances of elementary templates. The number of conflicts for accessing an S-node instance of template V is O ` S p M log M + c ' and the memory load is 1 + o(1) where load is defined as the ratio between the maximum and minimum number of data items mapped onto each memory module. 1. In...
